The minhag pashut (common custom) is to tell someone else about the rainbow. That which the Kaf Hachaim and others say that it is like telling bad things, I don't agree with. It's the opposite; we are thanking Hashem for keeping us alive and not punishing us like we deserve. Also, seeing the rainbow brings persons to tshuva when they realise what a bad position the world is. Therefore it's correct for people to tell others.

I personally would say slightly different. If Hashem didn't want everyone to know about the rainbow, why show it just to a select few? Is it they who are the bad people and have to mend their ways while the others who don't see it themselves are all tsadikim and have no tshuva to do?

I like making a post where I can also provide some chiddush and not just repeat what others say.
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user2709Apr 30 '13 at 23:51

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+1, Thanks for taking the effort to make your answers clear and easy to read. (Have a look at how I have edited for ideas how to make things even clearer, which will result in making it easy for others to read, and thus upvoting).
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MichoelMay 1 '13 at 4:10

@Michoel Thank you very much. You must have taken quite some time to do this for me.
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user2709May 1 '13 at 4:15

As noted by Gershon, this is Mishnah Berurah citing the Chayei Adam. It seems that there might be room for manipulation according to other posekim. Thus:

Q. (252) Mr. Danny Persoff: Is there an Issur to look at a rainbow?
A. The Shulchan Aruch (229:1) writes that it is prohibited to look at a rainbow "B'yotair" for a prolonged period of time. The Gra (ibid.) writes that there is no prohibition of R'eeyah, briefly looking, for one needs to see the rainbow in order to make the Bracha; rather, the Issur is Histaklut, staring intently. (See also Machazit Hashekel ibid.) The Iyun Yaakov writes that it is a Mitzvah to see the rainbow in order to recite the Bracha. However, the Mishna Berura (229:1) quotes the Chayai Adam who maintains that one should not tell a friend that there is a rainbow in the sky.

Regarding the reason for the Issur, the Gemara (Baizah 16a) writes that the rainbow symbolizes the glory of Hashem, therefore, it is inappropriate to look at the rainbow just as it would be wrong to look at the glory of Hashem, K'veyachol. (See Shmot 24:10-11 regarding B'nai Yisrael looking at Elokai Yisrael.) The Tosfot Harid explains the comparison between a Keshet and Hashem: Just like the colors of a rainbow are indiscernible, one can not tell where one color ends and another begins, so too with regard to Hashem, we can not truly know Him, and we must symbolize that ignorance by abstaining from staring at the rainbow. (See the M'eeri Baizah16a, where he writes that the Issur is not to stare at the rainbow, rather, to delve into the mysteries of the Pesukim that deal with the rainbow in Parshat Noach.)

For instance, the Aruch HaShulchan, which some people pasken like over the Mishnah Berurah, writes in the same siman, 229 that the prohibition is just staring, not simply looking. And he does not cite the Chayei Adam about not telling a friend, and so does not bring it down lehalachah. This might well make sense, since you would not be causing your friend to violate any issur, if you are just telling him so that he can make the beracha.

Of course, consult your local Orthodox rabbi, who will in all likelihood tell you to follow the Mishnah Berurah. :)